your users need to actually get a license from your QlikView Server.
In order to do so, please make sure that you have either assigned a license to them manually in your QMC (licenses tab --> assigned CALs) or that "allow dynamcic CAL assignment" is enabled in the General tab of the licnenses tab.
To actually get the license to your user's local machine/client, your user should open his or her local QlikView Desktop Client and open a document directly from the server on the start page of QlikView.
To do so, go to the QV startpage and select any document via "open in server" - through this step your client will communicate with your QVS and actually acquire the license and not be a personal edition anymore as in your screenshot.
Hope this helps, let me know if you need anymore help with this.
I am new to QlikView, but still I will try to drop my 2 cents on your problem, just in case I might be of any help to you.
When you open the desktop client, in order to edit a document it has to be LOCAL to the application. You cannot edit a document when you open it with the "Open in Server..." functionality, i.e. when you access it on the remote server.
If you want to edit documents that you have on server, you have to make them somehow local to your desktop application. One solution that I follow is 1st to make the folder that contains my documents (on server) shareable 2) set the appropriate security options for people to be able to read/write and 3) on my desktop machine, to locate the folder using a windows explorer and make a Map Drive connection to create a local drive (e.g. Z: ) that is mapped to the shared folder. Then I open the document from desktop application as if it were local ("File/Open") and desktop client allows me to edit them.
I do not know whether this one helps.